Sigmund Freud!

He wrote "The Interpretation of Dreams", which is was his first work on the subject of dream interpretation. He sorted the mind into three different catgories: the "Id", which centered around the primal state. It focused on pleasure and desire and wish fulfillment, the "ego" which is the conscious and the rational state. This is the moral and more self-aware aspect of the mind, and finally the "superego" which is the censor for the id. It is also a major contributing factor for enforcing the moral codes of the ego. Freud reasoned that dreams were the only way that we were truly able to get a good look into our unconscious, or our id. He supported this idea with the idea that our guard is only truly down during the sleep state. He also says though that we need to have things represented symbolically so that we are not completely emptionally disturbed, since at times our dreams can be so psychologically harmful. He also states that we have trouble remembering our dreams because the superego has to do its job and protect our conscious mind from the disturbing images and thoughts that the unconscious mind produces during sleep. Freud helped us out in determining what our dreams meant by sorting out images into five different processes:
1. Displacement, which occurs when someone wants someone or something that is symbolized as someone or something else.
2. Projection, which ooccurs when the dreamer dumps everything that they want and desire onto another person.
3. Symbolization, which means that your urges that are repressed are acted out metaphorically.
4. Condensation, which is the process in which the person who is dreaming is hiding their feelings and urges by underplaying it into a breif dream image or event. The meaning of this dream is not at all obvious to the dreamer at first glance.
5. Rationalization, wich is when the dreaming mind organizes a dream that makes no sense into one that does make sense and is logical.
As with everything else, Sigmund Freud was convinced that sex was the reason that you dreamt what you did. He believed that every slender object or elongated object that appeared in a dream (knives, cigarettes, guns, pens, etc.) represented the phallus and and cavity (bowl, cave, tunnel, etc) represented the female geitalia.

Carl Jung!
He at first studied under the direction of Sigmud Freud but their different views on dreams caused them to eventually part ways. Though he did believe in the importance and the existance of the unconscious mind, he didn't view it as instinctual, animalistic, or sexual by any means. He saw it in a spiritaul way. He believed that dreams were a way or communicating and acquainting ourselves with the unconscious rather than an attempt to conceal our real feeling from the waking mind. They were a window into our unconscious, not a door to shut it out. They served as a guide to the waking mind to achieve wholeness and offered a solution to a problem that we are facing in our waking life. He believed that the ego that a person possessed was how one viewed themselves and how they portrayed themselves to the world. Part of his theory was that all things can be paired as opposites, quite like the yin-yang idea (good and evil, male and female, love and hate, etc). Therefore, the ego had to have a "counterego" which he referred to as the shadow. This represented the rejected aspects of yourself that you kept hidden and didn't wish to acknowledge. These are the more primative, uncultured, and awkward parts of ourselves.
Jung thought that images in dreams were a way of revealing something about ourselves, our realtionships with others, and situations in our waking lives. They not only guided our personal growth, but they helpwed us to achieve our potential as well. He believed that there is no wrong or right way to interpret a dream and that the meaning of your dream is on a personal level and up to personal judgement and up to how you interpret them. Whatever interpretation you feel right to you is the most significant and more important than what anyone else thinks or believes.
Carl Jung also noted a list of archetypes found in dreams including the trickster, the wise old man/woman etc. Check out the "film as modern mythology" page for more information on these archetypes!

Alfred Adler!
He believed that dreams were problem solving devices and that they needed to be brought to conscious light and interpreted and thought about in depth so that they could be better understood so that we could solve the problems in our waking lives. He believed that the more dreams we had and the more ofter we dreamt, the more problems we were likely to have. Therefore, the less dreams we had and the less often we dreamt, the less problems we had and the more "brain healthy" we are. Quite the opposite of Freud, Adler thought that control, power, and motivation, rather than sex and sexual urges were the reason for our dreams. He also didn't believe that our actions and behaviour in our waking life was ruled by our unconscious. He thought that rather, we strive for perfection and that the need for control is what causes us to do the things we do. He argued that we acted the same no matter what state we were in, unconscious or conscious, awake or asleep.
Adler believed that our dreams showed us what we truly thought and how we truly felt about a situation. They showed our true emotions and actions. In our dreams, we were able to very cleary see what our aggressions and impulses and desirese were. He saw our dreams as a way of overcompensating for the shortcomings in our waking life as well. Such as, if in real life a person is unable to stand up to their boss, he or she may very comfortable and safely lash out on their boss in a dream. Dreams provided a "safe-haven" for people to let out aggressions. They also offer some sort of satisfaction for a revenge of sorts, and are in most cases more socially acceptable than going into your office and stabbing your boss.